Q. 134.3( 247 Votes )

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships

Answer :



A and D are the two ships and the distance between the ships is AD. BC is the lighthouse and is the height of the lighthouse. observer is at point C
Give: BC = height of lighthouse = 75m

∠CAB = 45°,

∠CDB = 30°

To Find:  DA

In Δ ABC,

             
[ p = perpendicular and b = base of the right angled triangle]

AB=75 m                        [ tan 45º = 1]


In Δ CDB,


AD + AB= 75√3 m

DA = 75( √3 - 1) m 
Hence the distance between the ships is 75( √3 - 1) m

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
NCERT |  Imp. Qs. on Applications of TrigonometryNCERT |  Imp. Qs. on Applications of TrigonometryNCERT | Imp. Qs. on Applications of Trigonometry54 mins
Quiz | Applications of TrigonometryQuiz | Applications of TrigonometryQuiz | Applications of Trigonometry47 mins
Application of TrigonometryApplication of TrigonometryApplication of Trigonometry45 mins
RD Sharma | IMP Qs Discussion on Some Application of TrigonometryRD Sharma | IMP Qs Discussion on Some Application of TrigonometryRD Sharma | IMP Qs Discussion on Some Application of Trigonometry44 mins
Fundas of TrigonometryFundas of TrigonometryFundas of Trigonometry50 mins
Basic Concept of TrigonometryBasic Concept of TrigonometryBasic Concept of Trigonometry43 mins
Champ Quiz | Trigonometry Important QuestionsChamp Quiz | Trigonometry Important QuestionsChamp Quiz | Trigonometry Important Questions33 mins
Solving NCERT Questions on Trigonometric IdentitiesSolving NCERT Questions on Trigonometric IdentitiesSolving NCERT Questions on Trigonometric Identities56 mins
Smart Revision | Revise Trigo Like an ExpertSmart Revision | Revise Trigo Like an ExpertSmart Revision | Revise Trigo Like an Expert51 mins
NCERT I Trigonometric RatiosNCERT I Trigonometric RatiosNCERT I Trigonometric Ratios50 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses